堆排序的思想（以最小堆為例）：

• 給的無序數(shù)列，首先要將數(shù)組改造成符合最小堆
  • 關(guān)于最小堆的建造，從最后一個(gè)非葉結(jié)點(diǎn)開始，每個(gè)結(jié)點(diǎn)都向下調(diào)整
• 若要增加記錄，應(yīng)該加在數(shù)組的最后，然后對這個(gè)數(shù)向上調(diào)整，知直到找到合適的位置
• 若要?jiǎng)h除最小值，則只要將第一個(gè)與最后一個(gè)互換，數(shù)組長度減一，從堆頂向下調(diào)整
• 若要排序，則只要從最后一個(gè)數(shù)開始向前遍歷，遍歷到的每個(gè)數(shù)與堆頂互換后從堆頂向下調(diào)整，調(diào)整時(shí)數(shù)組末尾已排序好的數(shù)字不計(jì)入操作

#include <iostream>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <string>
#include <stdlib.h>
#include <math.h>
#include <vector>
#include <stack>
#include <queue>
#include <map>
#include <sstream>
using namespace std;

void heapDown(int nums[], int i, int n) {
    
    int temp = nums[i];
    int j = 2 * i + 1;
    while (j < n) {
        if (j + 1 < n && nums[j + 1] < nums[j]) {
            j = j + 1;
        }
        if (temp < nums[j]) break;
        nums[i] = nums[j];
        i = j;
        j = 2 * i + 1;
    }
    nums[i] = temp;
}

void heapUp(int nums[], int i) { //向上調(diào)整只有在增加數(shù)的時(shí)候用到
    int temp = nums[i];
    int j = (i - 1) / 2;
    while (j >= 0 && i != 0) {
        if (nums[j] <= temp) { //只需比較新加入的數(shù)與父結(jié)點(diǎn)
            break;
        }
        nums[i] = nums[j];
        i = j;
        j = (i - 1) / 2;
    }
    nums[i] = temp;
}

void createHeap(int nums[], int n) {
    int i;
    for (i = (n - 1) / 2; i >= 0; i--) { //從最后一個(gè)非葉子結(jié)點(diǎn)開始向下調(diào)整
        heapDown(nums, i, n);
    }
}

void deleteRootNum(int nums[], int n) {
    swap(nums[0], nums[n - 1]);
    heapDown(nums, 0, n - 1);
}

void addNum(int nums[], int n, int num) {
    nums[n-1] = num;
    heapUp(nums, n-1);
}

void heapSorted(int nums[], int n) {
    for (int i = n - 1; i >= 0; i--) {
        swap(nums[i], nums[0]);
        heapDown(nums, 0, i);
    }
}

void print(string str, int nums[], int n) {
    cout<<str<<endl;
    for (int i = 0; i < n; i++) {
        cout<<nums[i]<<" ";
    }
    cout<<endl;
}

int main() {
    int n = 10;
    int nums[11] = {9, 12, 17, 30, 50, 20, 60, 65, 4, 19};
    
    createHeap(nums, n);
    print("將數(shù)組修改成最小堆:", nums, n);
    
    n = n + 1;
    addNum(nums, n, 10);
    print("插入10:", nums, n);
    
    
    deleteRootNum(nums, n);
    n = n - 1;
    print("刪除了最小值:", nums, n);
    
    heapSorted(nums, n);
    //由于每次將最小的數(shù)放到最后，所以最小堆輸出的數(shù)組是遞增的
    print("將數(shù)組排序:", nums, n);
    
    return 0;
}